The Schur measure of Okounkov [1]}, along with its slightly richer cousin — the Schur process of Okounkov and Reshetikhin [2]} — have, in the past twenty years, provided rich interplay between combinatorics, probability, statistical mechanics, and enumerative geometry. They are measures on partitions or sequences of partitions for which one can compute all correlation functions as determinants [1]}, [2]}, [5]}, [6]} — in particular they yield rich sources of determinantal point processes. In most cases one can use simple steepest descent asymptotic analysis to study thermodynamic limits. This has been achieved for problems such as: distributions of longest increasing subsequences in random permutations [7]}, [8]}, [9]} and random words [10]}; asymptotics of currents in the totally asymmetric simple exclusion process (TASEP) with both wedge and flat initial conditions [11]}, [12]}, [13]}; last passage percolation with iid geometric or exponential weights [11]}; last passage percolation with iid Bernoulli weights, poetically named oriented digital boiling [15]}; the arctic circle theorem for the Aztec diamond [16]} — but the approach has been implicitly used prior by Johansson [17]}; \(z\) -measures in the representation theory of the infinite symmetric group [18]}; plane partitions [2]}; and many others not listed here due to space constraints. We refer the reader to the review articles of Borodin–Petrov [20]} and Borodin–Gorin [21]} for probabilistic/statistical mechanical points of view; and to the (now surely dated) review of Okounkov [22]} for connections to enumerative geometry.
